CONVERGENCE OF ADAPTIVE EXTRA-PROXIMAL ALGORITHMS FOR EQUILIBRIUM PROBLEMS IN HADAMARD SPACES

Abstract

New iterative extra-proximal algorithms have been pro\-posed and investigated for approximate solution of problems of equilibrium in Hadamard metric spaces. The para\-meter update rule does not use the values of the Lipschitz constants of the bifunction. In contrast to the rules of the linear search type, it does not require calculations of the bifunction values at additional points. In addition, at the initial stages of the algorithms, the step size parameter can increase from iteration to iteration. For pseudo-monotone bifunctions of the Lipschitz type we proved convergence theorems. It is shown that the proposed algorithms are applicable to pseudo-monotone variational inequalities in Hilbert spaces.